Abstract: Let C
be a closed convex subset of a 2-uniformly Banach space E with the best smooth constant K
and be a k-strict pseudo-contraction on C with a fixed point, for some Given an initial guess consider
the Mann’s algorithmIt is proved that if the control
sequence is chosen so that andthen
the Mann iterative sequenceconverges
weakly to a fixed point of T.
Keywords and phrases: weak convergence, strict pseudo-contractive mapping, fixed point, uniformly smooth Banach spaces.
